$ \left(\dfrac{1}{64}\right)^{\frac{3}{2}}$
$= \left(\left(\dfrac{1}{64}\right)^{\frac{1}{2}}\right)^{3}$ To simplify $\left(\dfrac{1}{64}\right)^{\frac{1}{2}}$ , figure out what goes in the blank: $\left(? \right)^{2}=\dfrac{1}{64}$ To simplify $\left(\dfrac{1}{64}\right)^{\frac{1}{2}}$ , figure out what goes in the blank: $\left({\dfrac{1}{8}}\right)^{2}=\dfrac{1}{64}$ so $ \left(\dfrac{1}{64}\right)^{\frac{1}{2}}=\dfrac{1}{8}$ So $\left(\dfrac{1}{64}\right)^{\frac{3}{2}}=\left(\left(\dfrac{1}{64}\right)^{\frac{1}{2}}\right)^{3}=\left(\dfrac{1}{8}\right)^{3}$ $= \left(\dfrac{1}{8}\right)\cdot\left(\dfrac{1}{8}\right)\cdot \left(\dfrac{1}{8}\right)$ $= \dfrac{1}{64}\cdot\left(\dfrac{1}{8}\right)$ $= \dfrac{1}{512}$